Analysis of Variance
Department of Educational Psychology
Agenda
1 Overview and Introduction
2 The Central Limit Theorem for Sample Means
3 The Central Limit Theorem for Sums
4 Use of the Central Limit Theorem
5 Conclusion
The concept of the mean average has come up a lot in our previous lectures, from discussions on descriptive statistics through probability and random variables
We are going to connect means (and sums) with the central limit theorem (CLT), which is critical in understanding how our sample statistics connect with our population parameters
Agenda
1 Overview and Introduction
2 The Central Limit Theorem for Sample Means
3 The Central Limit Theorem for Sums
4 Use of the Central Limit Theorem
5 Conclusion
\[ z = \frac{\bar{x} - \mu_X}{(\frac{\sigma_X}{\sqrt{n}})} \]
\[ \bar{R} \sim N(250, \frac{50}{\sqrt{40}}) \]
\[ z = \frac{\bar{r} - 250}{(\frac{50}{\sqrt{40}})} \]
Agenda
1 Overview and Introduction
2 The Central Limit Theorem for Sample Means
3 The Central Limit Theorem for Sums
4 Use of the Central Limit Theorem
5 Conclusion
\[ \sum{X} ~ N((n)(\mu_X), (\sqrt{n})(\sigma_X)) \]
\[ z = \frac{\sum{x}-(n)(\mu_X)}{(\sqrt(n)(\sigma_X))} \]
Agenda
1 Overview and Introduction
2 The Central Limit Theorem for Sample Means
3 The Central Limit Theorem for Sums
4 Use of the Central Limit Theorem
5 Conclusion
Agenda
1 Overview and Introduction
2 The Central Limit Theorem for Sample Means
3 The Central Limit Theorem for Sums
4 Use of the Central Limit Theorem
5 Conclusion
The CLT serves as a critical concept building on probability and continuous, normal distributions
The CLT underlies why larger samples result in more accurate estimates of our population parameters in our sample statistics
The CLT implications and characteristics are useful in making sense of results from statistical hypothesis testing (more on this later!)
Module 7 Lecture - Factorial/Two-Way ANOVA || Analysis of Variance